The present invention provides a random copolymer that is used for manufacturing a tire having excellent rollability and wear resistance and that includes randomly arranged monomer units of a conjugated diene compound and of a non-conjugated olefin, a rubber composition containing the random copolymer, a cross-linked rubber composition obtained by crosslinking the rubber composition, and a tire manufactured by using the rubber composition or the cross-linked rubber composition. A copolymer of a conjugated diene compound and a non-conjugated olefin, including a random copolymer having randomly arranged monomer units of the conjugated diene compound and of the non-conjugated olefin, and containing, by more than 30 mol %, a unit derived from the conjugated diene compound.